Sub-ohmic two-level system representation of the Kondo effect

Abstract

It has been recently shown that the particle-hole symmetric Anderson impurity model can be mapped onto a $Z_2$ slave-spin theory without any need of additional constraints. Here we prove by means of Numerical Renormalization Group that the slave-spin behaves in this model like a two-level system coupled to a sub-ohmic dissipative environment. It follows that the $Z_2$ symmetry gets spontaneously broken at zero temperature, which we find can be identified with the on-set of Kondo coherence, being the Kondo temperature proportional to the square of the order parameter. Since the model is numerically solvable, the results are very enlightening on the role of quantum fluctuations beyond mean field in the context of slave-boson approaches to correlated electron models, an issue that has been attracting interest since the 80's. Finally, our results suggest as a by-product that the paramagnetic metal phase of the Hubbard model at half-filling, in infinite coordination lattices and at zero temperature, as described for instance by Dynamical Mean Field Theory, corresponds to a slave-spin theory with a spontaneous breakdown of a local $Z_2$ gauge symmetry.

4 pages, 5 figures

References in corpus (2)

• Orbital selective Mott transition in multi-band systems: slave-spin representation and dynamical mean-field theory
• Dynamically Generated Double Occupancy as a Probe of Cold Atom Systems

Cited by in corpus (11)

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• Non-equilibrium and non-homogeneous phenomena around a first-order quantum phase transition
• Nonequilibrium Dynamics Across an Impurity Quantum Critical Point
• Transport through a magnetic impurity: a slave-spin approach
• Benchmarking the simplest slave-particle theory with Hubbard dimer
• Manumitting slave-spins in the Anderson impurity model
• The Out-of-Equilibrium Time-Dependent Gutzwiller Approximation
• Slave-spin approach to the Anderson-Josephson quantum dot
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